The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components

Question :

Lifetimes (in hours)	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	10	35	52	61	38	29

The following (60 – 80) has the maximum frequency. Therefore, this is the modal class.

Here, l = 60, h = 20, \(f_1\) = 61, \(f_0\) = 52 and \(f_2\) = 38

Now, let us substitute these value in the formula

Mode = l + (\(f_1 – f_0\over 2f_1 – f_0 – f_2\))\(\times\)h

= 60 + (\(61 – 52\over 122 – 52 – 38\))\(\times\) 20

= 60 + \(9\over 32\) \(\times\) 20

= 60 + 5.625 = 65.625

Thus, the modal lifetimes of the components is 65.625 hours.